𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the discount sum of Bernoulli random variables

✍ Scribed by Ka-Sing Lau; Alan Ho

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
643 KB
Volume
63
Category
Article
ISSN
0378-3758

No coin nor oath required. For personal study only.

✦ Synopsis

Let {~,,},~1 be i.i.d. Bernoulli randoln variables. For Β½</,<1, let X ~.~i~1//',;, bc ,he discount sum and let Β’l/, be the distribution measure. It is known that if p ~ is a P.V. nmnber.

then I~:, is continuously singular. In this paper we use a Markov chain technique to obtain !he precise L:-dimension of such measures. In particular for O {,/'5 -1)/'2, we use a device of Strichartz et al. and the renewal equation to derive a formula for the L:'-dimension and :he entropy dimension of the corresponding /~/,. @ 1997 Elsevier Science B.V.

πŸ“œ SIMILAR VOLUMES

Comparing sums of independent bounded ra
Comparing sums of independent bounded random variables and sums of Bernoulli random variables
✍ Erich Berger πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 363 KB

This paper deals with the comparison of tail probabilities for sums of independent bounded random variables and those fbr sums of Bernoulli random variables. As a consequence, we obtain a new sufficient criterion for the strong law of large numbers for a certain class of sequences of independent ran

Sums of dependent Bernoulli random varia
Sums of dependent Bernoulli random variables and disease clustering
✍ Chang Yu; Daniel Zelterman πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 111 KB

We develop new discrete distributions that describe the behavior of a sum of dependent Bernoulli random variables. These distributions are motivated by the manner in which multiple individuals with a lung disease appear to cluster within the same family. General results for these models include recu